Ingots of metals generally consist of three zones of different shapes of grains (Fig. 1). The boundaries of the three zones can be determined, if we compare the inward propagation velocities of melting point υ_m=(_??_x/_??_t)_θ=θ_m with Tamman's “Kristallisationsgeschwindigkeit” KG at each point of ingots. A zone will be constituted with columnar grains, if therein KG_??_υ_m; and with granular grains, if therein KG<υ_m. The behaviours of vcurves in ingots are shown in Figs. 3 and 4. A simplified ideal case was calculated by solving the differential equation of thermal conduct ivity, and therefrom actual case was deduced. The reason why the values of υ_m excel both at surface and center of ingots is as fallows: at the surface as the cooling velocity _??_θ/_??_t is large, υ_m becomes prominent, and at the center as the thermal gradient _??_θ/_??_x is small, υ_m becomes again prominent. The relative positions of υ_m curve and KG curves are illustrated in Fig. 5. Four typycal cases are distinguishable.
(1) KGI: Ingot will be constituted entirely with columnar grains.
(2) KGII: Ingot will consist of two zones, the outer one (from surface to intersection of two curves) being constituted with columnar grains and the inner one (from intersection to center) with granular grains.
(3) KGIII: Ingot will consist of three zones, two intersections of two curves representing the boundaries of zones (Fig. 6).
(4) KGIV: Ingot will be constituted entirely with granular grains.
Inversely utilising this consideration, we shall be able to determine Tammann's KG curve, which is not yet determined numerically. The method is as follows: When the calculated υ_m curve cuts the boundaries of zones of cast ingot, then the intersections will furnish the points on KG curve. Repeating this process at various conditions of casting, we shall be able to gain the whole KG curve.

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Aluminium was meltedin a mild steel case heated at 670°, 700° and 950° verticalelectric furnace and the case was dipped in water. The Aluminium block solidified was then examined. It was found that the macro-structures were influenced by the cooling speed nad the milting temperature. By certain conditicns columnar crystals developes vertically from the bottom of the case. Such a condition varies with the melting temperature, and the higher the temperature, such structures developed in a wider range of cooling speed.

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Using 147 kinds of this ternary alloy, the equilibrium diagram has been thoroughly studied chiefly by thermal analysis and microscopic examination. In this ternary system, no ternary compound exists, while 3 binary compounds, Cu₂Cd, Cu₄Cd₃ and CuCd₃, 2 Ag-Cd binary solid solutions β and ε and 4 ternary solid solutions, Cu, Ag, δ and η exist. η ternary solid solution is formed by Cu₅Cd₈ and γ solid solutions. So there exist 9 primary crystallization surfaces and 14 monovariant curves, and along these curves the following reactions take place,
Mono-variant reactions:(1) M_??_Cu+Ag, (2) M+Ag_??_β, (3) M_??_β+Cu, (4) M+β_??_η,
(5) M_??_Cu+η, (6) M+Cu_??_Cu₂Cd, (7) M_??_Cu₂Cd+η, (8) M+Cu₂Cd_??_Cu₄Cd₃,
(9) M_??_η+Cu₄Cd₃, (10) M+η_??_δ, (11) M+η_??_CuCd₃, (12) M_??_CuCd₃+δ,
(13) M+δ_??_ε, (14) M_??_Cd+CuCd₃.
In this ternary system, there exist 5 non-variant points, at which the following reactions take place at temperatures given.
Non-variant reactions:
(1) M+Ag_??_β+Cu, (712°) (2) M+β_??_η+Cu (620°), (3) M+Cu_??_Cu₂Cd+η, (518°),
(4) M+Cu₂Cd_??_η+Cu₄Cd₃ (516°), (5) M+η_??_CuCd₃+δ (329°), (6) M+δ_??_CuCd₃+ε (318°).

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Regarding the quenching effects of ordinary chill-cast specimens of the copper-rich Be-Cu alloys the author had previously been investigated and reported⁽¹⁾. In the present research, the same effect has been observed by the microscopic, röntgengraphic and dilatometric methods, with regard to the variations of those effects due to the differences of the crystallized directions of the specimens.
The alloys containing 2.2%_??_4.4% of Be were cast into the mould, as shown in Fig. 2., designed to ensure the special mode of crystallization, and from the ingot thus obtained, two kinds of specimens, i.e. (B); the normally crystallized, and (A); the uni-directionally crystallized, were taken. Now, these two kinds of cast specimens were respectively normalized and quenched, and then the dilatometric changes during heating were differentially measured. As the results of these experiments, it was found that the quenched specimens indicate the most remarkable variations of changes, according to the direction of crystallization; For instance, vigorous expansion was observed as the quenching effect of the specimen (A), while, a servere contraction was found in the case of the specimen (B), though its composition is the same as (A).
It was elucidated that the cause of those variations of the dilatometric changes in both kinds of specimens, may be considered to rest on the difference of the orientation of α- and β-crystallites.
Moreover, the similar studies were repeated in connection with the rolled specimens of the same alloys.

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The influence of alloying elements for a peculiarity on extruded bars of Al alloys, as well as, the relation between the microstructure and heat treatment and the peculiarity have been examined mechanically and microscopically. The results obtained are summerised as follows: -
(1) In general, the peculiarity on extruded bar seems to appear on the Al alloys containing Mn or Cr, and it becomes more frequent with the increase of Mn or Cr content to the limit of its solid solubility at high temperature in Al, and also its stability increases with the rise of extruding temperature.
(2) A extruded bar with the peculiarity has a fibrous structure even when it is subjected to such a high temperature as the nominal quenching temperature, but it changes into a normal structure by heating at higher temperature or more prolonged heating; by the latter treatment the peculiarity disappears.
(3) The peculiarity always appears without presence of Mn or Cr, if alloys are quenched from such a temperature as they retain the characteristic fibrous structure and undergo hardening.
(4) The peculiarity may be regarded as a phenomenon which appears only in the Age hardenable Al alloy, because it occurs more frequent as the progress of Age-hardening and it does not almost appear in alloys of the annealed state.
(5) It is thus concluded from the results of the present investigation that the peculiarity on extruded bar of Al alloys containing such element as Mn or Cr is caused by the woked-structure based upon the special deformation in the cause of extrusion process, and the betted mechanical properties has been atribute to the slip interference effect and increasing dispertion degree of distorsion due to Age-hardening.

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With the same apparatus used in the previous experiment⁽¹⁾, the change of hardness of duralumin was observed during the course of fatigue progress under reversed bending, and the effect of aging on the recovery of hardness of the fatigued specimen was also studied. Duralumin was tested in annealed state and in quenched one.
In the course of fatigue process under continuous repetitions of stress, the hardness decreases at first and after passing through a minimum it increases with the increase of the number of repetitions. As the number of stress repetitions increases furthermore, the hardness change occurs in, the quite same manner as above, that is, it decreases to a minimum value and afterwards increases gradually with the increase of stress repetition. The initial decrease and the subsequent increase of hardness in the early stage of repetitions are caused by the change in the outer layer of the specimen, and those in the next stage are caused by the change in the inner portion of the specimen. The number of repetitions at which the minimum value of hardness occurs becomes less as the intensity of stress increases. Further, the amount of minimum hardness in the early stage becomes less as the stress intensity increases so, that the hardness increases at the first application of a stress, when it is of a comparatively high intensity.
As to the effect of aging at room temperature, on the recovery of hardness of the fatigued specimen, the following results were obtained. After the. application of stress of a constant intensity, the recovery of hardness takes place in two different manners according to the number of repetitions to which the specimen has been subjected, i.e., when the number of repetitions is small, the hardness of a fatigued specimen increases gradually with the lapse of time and becomes constant after a certain time, but when the number of stress repetitions is large, the hardness decreases first quickly and then slowly and at last it attains a constant value. The higher the intensity of stress, the number of repetitions becomes small, by which the decrease of hardness is resulted in the early period of the rest.
The author has explained the above changes of hardness under continuous repetitions of stress by a combined effect of the accumulation of internal stress and the loss of stability of structure. He has also explained the hardness change due to aging by a combined effect of the release of internal stress and the recovery of unstable structure.

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In the study of the “Relative Method” of the quantitative spectrum analysis, the following relation has been theoretically deduced with certain assumptions,
ΔS=qlogC_B+K'
where ΔS is the difference of the blackening of a pair of the spectrum lines to be compared, C_B the concentration of an element B to be determined, and q and K' are constants.
Various experiments are carried out with regard to the assumptions, and the adoptability of the proposed relation has been thoroughly tested.

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